Making a raised bed to house an existing cold frame

I have a cold frame where the base measures 30" x 72". I have 4 metal corners designed to hold 2" thick lumber to form a raised bed where the length of the wood determines the inside dimensions of the raised bed. I want the cold frame to sit inside the raised bed about 1" below the top. I plan to put a 1x1" strip on the inside of the long sides of the raised bed about one inch down to form a support for the cold frame. What I'm trying to determine is the lengths of the lumber used.

Two 30" pieces of 2x12 lumber plus two 72" pieces of 2x12 would be too small. Which of the following would be better
My concern with the 1/4 inch room all around is that the 1x1" rail, deprived of 1/4" will not be sufficient support for the cold frame.

Any suggestions?

 

How are you doing the top or roof of the cold frame? How you are constructing the top/roof will have a great affect on your 1 x 1 side rails but since they can only bow out 1/4" before they hit the sides of your raised bed they aren't going to bow much.

 

I purchased it
The bottom of the frame is made with 1x1's